How do you find the average value of a function on a surface?

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To find the average value of the function (1+4z)**3 on a surface, one must compute the surface integral of the function over the area of the surface. The average value is determined by dividing this integral by the total area of the surface. This approach clarifies the process of calculating the average value on a surface. Understanding the relationship between the surface integral and the area is crucial for solving the problem effectively. The discussion emphasizes the importance of these mathematical concepts in finding the average value.
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Homework Statement


find the average value of (1+4z)**3 on the surface ...


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The Attempt at a Solution


All I really want to know is how to go about this? Is the average value on the surface just the surface integral over the area of (1+4z)**3?
 
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It's the integral of (1+4z)^3 over the surface divided by the area of the surface.
 
thank you, that makes more sense
 

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